(1) We extend the work in [1]} into the partially observed case with random jumps. There exist correlated noises between the state equation and the observation equation, which make the original decoupled forward-backward stochastic system become a kind of fully-coupled one. We first prove the existence and uniqueness of the solution to fully coupled FBSDEPs in \(L^2\) -space. However, due to some technical difficulties, we only obtain the existence and uniqueness of the solution to the fully coupled FBSDEPs and give its estimate under (A4), (A6) in \(L^\beta \) -space, for \(\beta \ge 2\) . For further resolve the difficulties, we relax the Assumption (A6), and obtain the existence and uniqueness of the solution to fully coupled FBSDEPs and give its estimate under (A4), (A5) by defined a new space \(\tilde{F}^{2,\beta }[0,T]\) .
